Mathematics Tes...

In the given circle, \(O\) is the centre and length of chord \(X Y=\) length of chord \(Z W\). If \(\angle\) \(X O Y=60^{\circ}\), then what is the measure of \(\angle Z O W\) ?

If \(\tan \theta=\frac{1}{\sqrt{7}}\) then \(\frac{\operatorname{cosec}^{2} \theta-\sec ^2 \theta}{\operatorname{cosec}^2 \theta+\sec ^2 \theta}=\)

Find the sum of the series \(3+\frac{9}{2}+6+\frac{15}{2}+\ldots\) upto \(25^{\text {th }}\) term.

If the latus rectum of an ellipse is equal to half of its minor axis, then its eccentricity is:

The equation of a circle with diameters are 2x - 3y + 12 = 0 and x + 4y - 5 = 0 and area of 154 sq. units is:

A dice is thrown. Find the probability of getting an even number.

If \(A=\left[\begin{array}{cc}4 & x+2 \\ 2 x-3 & x+1\end{array}\right]\) is symmetric, then what is \(x\) equal to:

In a parallelogram \(O A B C\), vectors \(\vec{a}, \vec{b}, \vec{c}\) are, respectively, the position vectors of vertices \(A, B, C\) with reference to \(O\) as origin. A point \(E\) is taken on the side \(BC\) which divides it in the ratio of \(2: 1\). Also, the line segment \(A E\) intersects the line bisecting the angle \(\angle A O C\) internally at point \(P\). If \(C P\) when extended meets \(A B\) in point \(F\), then the position vector of point \(P\) is:

If \(a_{1}, a_{2}, a_{3}\) and \(a_{4}\) are 4 consecutive terms in the expansion of \((1+x)^{n}\), then \(\frac{a_{1}}{a_{1}+a_{2}}+\frac{a_{3}}{a_{3}+a_{4}}=\) ?

If \(\int_{0}^{a}[f(x)+f(-x)] d x=\int_{-a}^{a} g(x) d x\), then what is \(g(x)\) equal to?